Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 6.O₇(3)

Name:

6.O7(3)

Group order:

27512110080 = 2¹⁰ ⋅ 3¹⁰ ⋅ 5 ⋅ 7 ⋅ 13

Number of classes:

180

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Maximal subgroups:

	Order	Index	Structure	Name
1	78382080	351	121.U4(3).22	12_1.U4(3).2_2
2	75582720	364	6.(35:U4(2):2)	6.(3^5:U4(2):2)
3	72783360	378	3 × 2.L4(3).22	3x2.L4(3).2_2
4	25474176	1080	2 × 3.G2(3)	2x3.G2(3)
5	25474176	1080	2 × 3.G2(3)	6.O7(3)M5
6	24564384	1120	2 × 3.(33+3:L3(3))	2x3.(3^(3+3):L3(3))
7	8709120	3159	3 × 2.S6(2)	3x2.S6(2)
8	8709120	3159	3 × 2.S6(2)	6.O7(3)M8
9	7558272	3640	6.31+6+.(2A4 × A4).2	6.O7(3)M9
10	2177280	12636	3 × Isoclinic(2.A9.2)	3xIsoclinic(2.A9.2)
11	2177280	12636	3 × Isoclinic(2.A9.2)	6.O7(3)M11
12	1244160	22113	3 × 2.(22 × U4(2)).2	3x2.(2^2xU4(2)).2
13	967680	28431	21+6+:3A7	2^(1+6)_+:3A7
14	103680	265356	3 × 2.(S6 × S4)	3x2.(S6xS4)
15	82944	331695	6.(A4 × 2(A4 × A4).2).2	6.(A4x2(A4xA4).2).2

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
13	dec. matrix (PDF)

Atlas representations:

2 available

Group constructions in GAP:

AtlasGroup( "6.O7(3)" )

Stored class fusions from this table:

2.O₇(3), 3.O₇(3), 6.O₇(3).2, O₇(3)

Stored class fusions to this table:

2¹⁺⁶₊:3A₇, 2 × 3.(3³⁺³:L₃(3)), 2 × 3.G₂(3), 3 × 2.(2² × U₄(2)).2, 3 × 2.(S₆ × S₄), 3 × 2.L₄(3).2₂, 3 × 2.S₆(2), 3 × Isoclinic(2.A₉.2), 6.(3⁵:U₄(2):2), 6.(A₄ × 2(A₄ × A₄).2).2, 2 × 3.G₂(3), 3 × 2.S₆(2), 6.3¹⁺⁶₊.(2A₄ × A₄).2, 3 × Isoclinic(2.A₉.2), 12₁.U₄(3).2₂

File created automatically by GAP on 13-Mar-2024.